A small current carrying loop having current i is placed in the plane of paper as shown. Another semicircular loop having current i₀ is placed concentrically in the same plane as that of small loop, the radius of semicircular loop is R(R a)

Question

A small current carrying loop having current i is placed in the plane of paper as shown. Another semicircular loop having current i₀ is placed concentrically in the same plane as that of small loop, the radius of semicircular loop is R(R a) . Find the force applied by the smaller ring on bigger ring in newton. (Given R=1 ~m , i=i₀= 40 ₀ A, a=0.1 ~m )

Quantrex Academy · Accepted Answer

Correct answer: 8

Magnetic field due to small ring at distance R from the centre B= ₀ 4 M R^3 where M=i a^2 B= ₀ 4 i a^2 R^3 = ₀ i a^2 4 R^3 d F=i₀ R d ₀ i^2 4 R^3 dF _ x = dF = ₀ i ₀ i ^2 d 4 R ^2 F_x= ₀ i₀ i ^2 4 R^2 ₀^ d _x= ₀ i i₀ a^2 4 R^2 2F_x= ₀ i i₀ a^2 2 R^2 F_y=0 F_ net =F_x= ₀ i₀ i ₀ a^2 2 R^2 = 8 Newton.

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